Question

the metallic radius of an aluminum atom is 143 pm. what is the volume of an aluminum atom in cubic meters? m³

Explanation:

Step1: Convert picometers to meters

We know that $1\ pm = 1\times10^{- 12}\ m$. So, if the radius $r = 143\ pm$, then $r=143\times10^{-12}\ m$.

Step2: Use the volume - formula for a sphere

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 143\times10^{-12}\ m$ into the formula:
\[

$$\begin{align*} V&=\frac{4}{3}\pi(143\times 10^{-12})^{3}\\ &=\frac{4}{3}\pi\times(143^{3})\times(10^{-12\times3})\\ &=\frac{4}{3}\pi\times2924207\times10^{- 36}\\ &=\frac{4\times\pi\times2924207}{3}\times10^{-36}\\ &\approx\frac{4\times3.14\times2924207}{3}\times10^{-36}\\ &=\frac{36755294.96}{3}\times10^{-36}\\ &\approx1.2251765\times10^{-29}\ m^{3} \end{align*}$$

\]

Answer:

$1.23\times 10^{-29}\ m^{3}$